Infrared radiation and planetary temperature

ergy from the Sun. Distributed uniformly over the mass of the planet, the absorbed energy would raise Earth’s temperature to nearly 800 000 K after a billion years, if Earth had no way of getting rid of it. For a planet sitting in the nearvacuum of outer space, the only way to lose energy at a significant rate is through emission of electromagnetic radiation, which occurs primarily in the subrange of the IR spectrum with wavelengths of 5–50 μm for planets with temperatures between about 50 K and 1000 K. For purposes of this article, that subrange is called the thermal IR. The key role of the energy balance between short-wave solar absorption and long-wave IR emission was first recognized in 1827 by Joseph Fourier,1,2 about a quarter century after IR radiation was discovered by William Herschel. As Fourier also recognized, the rate at which electromagnetic radiation escapes to space is strongly affected by the intervening atmosphere. With those insights, Fourier set in motion a program in planetary climate that would take more than a century to bring to fruition. Radiative transfer is the theory that enables the above to be made precise. It is a remarkably productive theory that builds on two centuries of work by many of the leading lights of physics. Apart from its role in the energy balance of planets and stars, it lies at the heart of all forms of remote sensing and astronomy used to observe planets, stars, and the universe as a whole. It is woven through a vast range of devices that are part of modern life, from microwave ovens to heatseeking missiles. This article focuses on thermal IR radiative transfer in planetary atmospheres and its consequences for planetary temperature. Those aspects of the theory are of particular current interest, because they are central to the calculations predicting that global climate disruption arises from anthropogenic emission of carbon dioxide and other radiatively active gases. An atmosphere is a mixed gas of matter and photons. Radiative transfer deals with the nonequilibrium thermo dynamics of a radiation field interacting with matter and the transport of energy by the photon component of the atmosphere. Except in the tenuous outer reaches of atmospheres, the matter can generally be divided into parcels containing enough molecules for thermodynamics to apply but small enough to be regarded as isothermal and hence in local thermo dynamic equilibrium (LTE). The local radiation field need not be in thermodynamic equilibrium with matter at the local temperature. Nonetheless, the equations predict that the radiation field comes into thermodynamic equilibrium in the limiting case in which it interacts very strongly with the matter. For such blackbody radiation, the distribution of energy flux over frequency is given by a universal expression known as the Planck function B(ν,T ), where ν is the frequency and T is the temperature. Integrating the Planck function over all directions and frequencies yields the Stefan–Boltzmann law for the flux F exiting from the surface of a blackbody, F = σT 4, where σ = 2πkB/(15ch) ≈ 5.67 × 10−8 W m−2 K−4. Here, kB is the Boltzmann thermodynamic constant, c is the speed of light, and h is Planck’s constant. The fourthpower increase of flux with temperature is the main feedback allowing planets or stars to come into equilibrium with their energy source. Since such bodies are not actually isothermal, there is a question as to which T to use in computing the flux escaping to space. Radiative transfer is the tool that provides the answer. The appearance of h and c in the Stefan–Boltzmann constant means that relativity and quantization—the two nonclassical aspects of the universe—are manifest macroscopically in things as basic as the temperatures of planets and stars. It is intriguing to note that one can construct a universe that is classical with regard to quantization but nonetheless is well behaved with regard to the thermodynamics of radiation only if one also makes the universe classical with regard to relativity. That is, σ remains fixed if we let h → 0 but also let c tend to infinity as h−3/2.